In case of personal injury, all claims for compensation shall be forever barred unless, within two years after the accident, the parties shall have agreed upon the compensation payable under the Nebraska Workers’ Compensation Act, or unless, within two years after the accident, one of the parties shall have filed a petition as provided in section 48-173. In case of death, all claims for compensation shall be forever barred unless, within two years after the death, the parties shall have agreed upon the compensation under the Nebraska Workers’ Compensation Act, or unless, within two years after the death, one of the parties shall have filed a petition as provided in section 48-173. When payments of compensation have been made in any case, such limitation shall not take effect until the expiration of two years from the time of the making of the last payment. In the event of legal disability of an injured employee or his or her dependent such limitation shall not take effect until the expiration of two years from the time of removal of such legal disability.